Upvote:10
You have been directly instructed by the UK Embassy to do so, so yes, of course you should. Fill out the request. Always follow the instructions given to you by embassy/consulate staff in situations like this.
If yes, Is it only the standard subject access request form which I should fill in or should I fill in additional documents?
Fill out the document(s) that were referred to in the email you mentioned in OP. If only the "standard subject access request" was mentioned, then that is enough. You will then be given a copy of the rejection letter, with which you can proceed with the new application. Continue to follow the instructions of the staff.